ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Why Is Algebra Important to Know

Updated on May 1, 2019
Paul Kuehn profile image

Math has always been one of Paul's favorite subjects in school. In high school, Paul studied 2 years of algebra and has used it every day.

Why Is Algebra Important to Know

Uses of Algebra
Uses of Algebra | Source

Algebra is one of the most important subjects you will learn in school. Its applications will not only help you solve equations and word problems in class but also be of great use in daily life.

My dad often said that if you can express your ideas in mathematics, you really know what you are talking about. Dad was actually referring to algebra a part of mathematics which uses letters and other symbols to represent numbers and quantities in formulae and equations.

In this article, I will first give examples of how algebra can be used in the classroom to solve word problems. Next, I will cite different ways of how algebra can be applied to daily life.

What Is Algebra?

Algebra is a discipline of mathematics that students learn after mastering addition, subtraction, multiplication, division, fractions, and decimals in arithmetic.

I started learning algebra in the ninth grade in 1958. Students today begin learning at an earlier grade. When I was teaching English in a Thailand school in 2012, students were starting to learn algebra in the fifth and sixth grades.

In algebra, letters like x and y and other symbols are used to represent numbers and quantities in formulae and equations.

Invention of Algebra

According to the website Aljazeera, Muhammed ibn Musa Al-Khwarizmi, a ninth-century Muslim mathematician and astronomer, is the father of algebra. The word algebra is derived from the title of his book, Kitab al-Jabr.

Importance of Algebra

Basic algebraic principles are applied in other math courses such as geometry, trigonometry, and calculus. In addition, algebra can be used to solve practical word problems in all other math problems using formulae and equations.

Applying Algebra to Solve Word Problems in the Classroom

Here are two examples of how algebra can be used to solve word problems.

1. Age Problems

Let's say we have a word problem stated like this. There are two persons, Peter and Paul. Peter is older than Paul. The sum of their ages is 30 and the difference is 6. How old are Peter and Paul?

In solving a word problem, the first step is to ask what information is being sought. Clearly, the question wants to know the ages of Peter and Paul. We know that Peter is older than Paul.

Using algebra, we use x to represent the age of Peter and use y to represent the age of Paul. The sum of their ages is 30 can be represented using x + y = 30. The difference of their ages is 6 can be represented with the equation x - y = 6.

We then solve the two equations by adding them to find the values of x and y.

x + y = 30

x - y = 6

2x = 36

x = 18

We find that x or Peter is 18. By substituting 18 for x in the equation x + y = 30,

18 + y = 30, we solve and find that y = 12. Paul is thus 12.

We check our answers by substituting the ages of Peter and Paul in the equations.

18 + 12 = 30

18 - 12 = 6

2. Trigonometry Problem

Let's now look at this problem. Assume that we have a right triangle in which the base is 4 and the height 3. The problem is to determine the length of the hypotenuse.

In solving this problem, we must understand the Pythagorean Theorem which states that the sum of the base squared and height squared equals the hypotenuse squared.

If the base is represented by a, the height by b, and the hypotenuse by c, we can express the Pythagorean Theorem as a2 + b2 = c2.

In solving for the length of the hypotenuse or c, we substitute the known values of the base and height into the equation as

4 squared + 3 squared = c2

In solving this equation we get

16 + 9 = c2

25 = c2

By taking the square root of both sides of the equation, we get

5 = c in which c is the length of the hypotenuse.

Applying Algebra to Daily Life

Many countries of the world express temperature in degrees Celsius unlike degrees Fahrenheit used in the United States.

if the temperature is, for example, 30 degrees Celsius in Thailand, what is this equivalent to in Fahrenheit degrees?

To solve this problem, we must know that degrees Fahrenheit equals 1.8 times degrees Celsius plus 32 degrees. This is expressed in equation form as

F degrees = 1.8 x C degrees + 32 degrees

Substituting 30 degrees Celsius into this equation we get

F degrees = 1.8 x 30 degrees + 32 degrees or

F degrees = 54 degrees + 32 degrees

F degrees = 86 degrees

Hence we have determined that 30 degrees Celsius equals 86 degrees Fahrenheit.

Another application of algebra to daily life is in using equivalent ratios. I encountered the following problem when giving a test as a teacher in Thailand. The test which I had composed had 60 questions on it. If a student, for example, had 22 questions correct, what was his percentage score?

In solving this problem, we must understand that percentages are based on 100. We can set up equivalent ratios to solve this problem as follows

x/100 = 22/60 where x is the score based on percentage points

By cross multiplying in solving this equation we get

x(60) = 22(100)

60x = 2200 By dividing both sides of the equation by 60, we arrive at

x = 36.6 or 37 percent as the score on the test.

These are only two examples showing how algebra can be applied to daily life. People will encounter many more in their lives. Algebra is definitely important to know in life.


© 2019 Paul Richard Kuehn

Comments

    0 of 8192 characters used
    Post Comment
    • Paul Kuehn profile imageAUTHOR

      Paul Richard Kuehn 

      5 months ago from Udorn City, Thailand

      Thank you very much for your suggestions, George.

    • verdict profile image

      George Dimitriadis 

      5 months ago from Templestowe

      Hi.

      You have covered some important areas of mathematics involving algebraic manipulation. Some suggestions:

      Pythagoras' theorem is not really part of trigonometry because only side lengths of a triangle are used, not angles. Hence it might be better to use THEOREM OF PYTHAGORAS.

      A diagram illustrating Pythagoras' Theorem might be useful.

      Show powers of 2 as raised numbers or as, for example, a^2+b^2=c^2

      After x/100=22/60 you can multiply by 100 to get x=100*22/60

      Regards

      George

    • Paul Kuehn profile imageAUTHOR

      Paul Richard Kuehn 

      5 months ago from Udorn City, Thailand

      Thanks for the very nice comment, Pamela. My father was using algebra well into his 80s.

    • Pamela99 profile image

      Pamela Oglesby 

      5 months ago from Sunny Florida

      I was one of the few girls in school that liked algebra. I found myself using algebraic formulas working in the ICU as a RN. So often children don't think they need to learn various subjets, but this is an important cass. I think this is a very good article.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)